The present invention relates to an achromatic lens to be used as a collimator lens, or an objective lens for a telescope. Particularly, the present invention relates to a diffractive/refractive achromatic lens that includes a refractive lens system provided with a diffractive grating.
Conventionally, an achromatic lens has been well known and used as a collimator lens or an objective lens. An example of the achromatic lens employs two thin lenses: one being a lens having large positive power that is made from crown glass having relatively low dispersion; and the other being a lens having small negative power that is made from flint glass having relatively high dispersion. The resultant power is therefore positive, while the dispersion is neutralized.
Since optical glass has dispersion such that refractive index thereof increases with decreasing wavelength of light, a positive refractive lens has longitudinal chromatic aberration where a back focus of the lens decreases as wavelength becomes shorter. The achromatic doublet corrects the chromatic aberration of the positive lens by using a negative lens that has opposite chromatic aberration.
The conventional achromatic doublet is designed for correcting the longitudinal chromatic aberration with respect to two different wavelengths, e.g., F-line (486 nm) and C-line (656 nm). That is, the light beams of F-line and C-line are focused on substantially the same focal point.
However, light beams having wavelengths except the C- and F-lines are not focused on the same focal point. Particularly, the back focus of the doublet becomes remarkably larger in a range shorter than F-line. This remaining chromatic aberration is called as secondary spectrum.
If the normal optical glasses are used for constituting the conventional type of the achromatic lens, it is impossible to correct the secondary spectrum sufficiently. Because refractive index of glass increases as wavelength becomes shorter as described, while increasing degree of the flint glass is larger than that of the crown glass in short wavelength range. Then the chromatic aberration of the doublet is overcorrected (backfocus becomes too long) in the range shorter than F-line.
In order to suppress the secondary spectrum of the longitudinal chromatic aberration with the conventional type of the achromatic lens, fluorite or anomalous dispersion glass should be used. However, these materials are too expensive.
It is therefore an object of the present invention to provide an achromatic lens., which is capable of correcting the secondary spectrum of the longitudinal chromatic aberration without using expensive material such as the fluorite or anomalous dispersion glass.
For the above object, according to the present invention, there is provided a diffractive-refractive achromatic lens that includes a refractive lens system exhibiting longitudinal chromatic aberration that is substantially proportional to wavelength such that the back focus of the refractive lens system decreases as the wavelength becomes shorter, and a positive diffractive grating for correcting the longitudinal chromatic aberration of the refractive lens system.
The refractive lens system having such a chromatic aberration includes a positive lens having relatively small dispersion and a negative lens having relatively large dispersion. Further, the following condition (1) should be satisfied:
0.005 less than f/fD less than 0.2xe2x80x83xe2x80x83(1)
where
f is a focal length of the entire lens system, and
fD a is focal length of the positive diffractive grating.
Preferably, the diffractive grating may be designed so that the following condition (2) is satisfied:
xe2x80x83xe2x88x920.05 less than P4/P2 less than 0.0xe2x80x83xe2x80x83(2)
where
P2 and P4 are diffractive coefficients of second and fourth orders when the diffractive grating is expressed by the following optical path difference function "PHgr"(h):
"PHgr"(h)=(P2h2+P4h4+ . . . )xxcex
where
h is a height from the optical axis, and
xcex is a design wavelength of the diffractive grating.
Embodiments described in this specification includes three groups. In a first group of the embodiments, the refractive lens system includes a non-achromatic doublet. In the second and third groups of embodiments, the refractive lens system consists of a combination of a refractive achromatic lens and an additional lens. In each case, the diffractive grating could be formed on one surface of the refractive lenses or provided as a separate diffractive element.
In the first group of the embodiments, the doublet should have longitudinal chromatic aberration such that the back focus of the refractive lens system decreases as the wavelength becomes shorter. In such a case, it is preferable that the refractive lens system satisfies the following condition (3);                     0.001         less than                               f            c                    ·                                    ∑                              i                =                1                            m                        ⁢                          xe2x80x83                        ⁢                          1                                                f                  i                                ·                                  v                  i                                                                     less than         0.02                            (        3        )            
where
fc is a focal length of the refractive lens system,
fi is a focal length of an i-th lens of the refractive lens system counted from the object side,
xcexdi is an Abbe number of the i-th lens of the refractive lens system counted from the object side, and
m is a total number of lenses of the refractive lens system.
In the second and third groups of the embodiments, the refractive achromatic lens is corrected in chromatic aberration at two different wavelengths and an additional refractive lens generates longitudinal chromatic aberration such that the back focus of the refractive lens system decreases as the wavelength becomes shorter. In such a case, it is preferable that the refractive achromatic lens satisfies the following condition (4);                               "LeftBracketingBar"                                    f              I                        ·                                          ∑                                  i                  =                  1                                m                            ⁢                              xe2x80x83                            ⁢                              1                                                      f                    i                                    ·                                      v                    i                                                                                "RightBracketingBar"                 less than         0.002                            (        4        )            
where
fI is a focal length of the refractive achromatic lens,
fi is a focal length of an i-th lens of the refractive achromatic lens counted from the object side,
xcexdi is an Abbe number of the i-th lens of the refractive achromatic lens counted from the object side, and
m is a total number of lenses of the refractive achromatic lens.
In the second group of the embodiments, the additional refractive lens is an additional positive lens. In such a case, it is preferable that the additional positive lens satisfies the following condition (5):
0.05 less than (fpxc2x7xcexdp)/f less than 0.5xe2x80x83xe2x80x83(5)
where
fp is a focal length of the additional positive lens, and
xcexdp is an Abbe number of the additional positive lens.
In the third group of the embodiment, the additional lens and the diffractive grating are arranged at a convergent side of the refractive achromatic lens, and the additional refractive lens includes a lens having a convex surface directed to the refractive achromatic lens. In such a case, it is preferable that the lens having the convex surface satisfies the following conditions (6) and (7);
0.01 less than rII1/(fIxe2x88x92L) less than 0.5xe2x80x83xe2x80x83(6)
0.01 less than dII/f less than 0.1xe2x80x83xe2x80x83(7)
where
rII1 is a radius of curvature of the convex surface,
L is an air gap along the optical axis between the refractive achromatic lens and the additional refractive lens, and
dII is a thickness of the lens having the convex surface.
The convergent side is defined as the side where the light beam is convergent. For example, the convergent side is an incident side when the invention is applied to a collimator lens, and an image side when the invention is applied to the objective lens.
In any groups of the embodiments, when the diffractive grating is formed on the optical element, which may be a separate element from the refractive lens system or the additional refractive lens, that is arranged at a convergent side of the refractive lens system, it is preferable that the following condition (8) is satisfied;
0.4 less than L/f less than 0.9xe2x80x83xe2x80x83(8)
where
L is an air gap along the optical axis between the non-achromatic doublet and the diffractive element (for the first group of the embodiments) or an air gap along the optical axis between the refractive achromatic lens and the additional refractive lens (for the second and third groups of the embodiments).
In the second and third groups of the embodiments, a conventional achromatic lens can be used as the refractive achromatic lens. In the other words, the combination of the additional refractive lens and the diffractive grating can be used as an attachment for the conventional achromatic lens to reduce the secondary spectrum of the longitudinal chromatic aberration.